The formation of gas giants and ice giants
by pebble accretion
Michiel Lambrechts
Anders Johansen / Alessandro Morbidelli
Observatoire de la côte d’azur
Exoplanets in Lund 6-8 May 2015
1
Planets and pebbles in protoplanetary discs
(1) Planets form in protoplanetary discs (few Myr, in wide circular orbits, and in multiples)
(2) Simultaneously, there is a large solid component in pebbles (mm-dm sized particles)
HD100546, 2Msol,~5Myr.
- 400 AU wide ppd
- potential imaged gas giant
planet at 53 AU
(Quanz et al 2014)
50AU
HL tau
TW Hya ppd (~5Myr) [left]
- 80 AU planet of 6-28 ME
- ~180--300 Me in pebbles
(Wilner+2005, bergin+2013)
2
Debes et al 2013
ALMA collaboration+, 2015
HL tau ppd (~1Myr) [right]
- formation of planets in
a ~1Myr old disc
- large pebble component (Greaves et al 2008)
2
Pebble accretion dynamics 1
Bondi pebble accretion
Lambrechts & Johansen, 2012
3
3
Pebble accretion dynamics 2
Hill pebble accretion
Lambrechts & Johansen, 2012
- Hill regime starts above a transition
mass:
⇣ r ⌘3/4
Mt ⇡ 3 ⇥ 10 3
M
5AU
- accretion occurs from the full Hill radius
- relative velocities are set by the
Keplerian shear (independent of
)
4
4
Pebble accretion dynamics 2
Hill pebble accretion
Lambrechts & Johansen, 2012
- Hill regime starts above a transition
mass:
⇣ r ⌘3/4
Mt ⇡ 3 ⇥ 10 3
M
5AU
- accretion occurs from the full Hill radius
- relative velocities are set by the
Keplerian shear (independent of
)
4
4
Difference with planetesimals
Ṁpeb ⇠ rH vH ⌃peb
Ṁplan ⇠
2
racc vH ⇢plan
⇢plan ⇠ ⌃plan /hplan
hplan ⇠ vH /⌦K ⇠ rH
Ṁpeb ⇠ rH vH ⌃peb
MMSN scaling
5
See also:
Ormel & Klahr 2010
Rafikov 2004 planetesimals/fragments
and Levison et al 2010
5
An analytic “toy model”
Lambrechts and Johansen, 2014




Birnstiel et al, 2012
⌃p (r, t)
+

⌧f (r, t)
Ṁc,p (r, t) ⇡


2(⌧f /0.1)
2/3
rH v H ⌃p

6
6
Pebble drift planets
Lambrechts and Johansen, 2014
- start with compact configuration of 4 embryos
- few Myr in disc with pebble surface density
reduced by a factor ~5 with respect to MMSN
- inside out planet formation
- pebble flux filtering
Ṁc
5 ⇣ ⌧f ⌘ 1/3 1 ⇣ rH ⌘2
f=
=
⌘
⇡
0.1
r
ṀF
⇣ ⌧ ⌘ 1/3 ✓ M ◆2/3 ⇣ r ⌘
f
c
⇡ 0.034
0.1
ME
10 AU
1/2
17% for one core and about 50% for a
‘Solar System’
- mass budget:
total mass: ~120-160 Me
terrestrial mass: 50 Me/2 (inside the ice line)
7
7
Characteristics of the model
- overcome type I migration
ice giants form ~ in situ
For
-> cross over mass
t!
r
e
B
y
b
lk
a
t
re
o
m
- steep initial dust-to-gas ratio dependency
8
Bucchave et al, 2012
8
The core accretion scenario
wi
s
e
l
bb
e
p
th
Core accretion with pebbles:
- rapid formation of the core without
enhancements of the solid surface density
- faster contraction of the gaseous envelope,
because of pebble isolation mass
50
Envelope
Core
growth growth
40
- particular attention at forming ice giants
Runaway
gas accretion
M /ME
30
20
Mc
10
0
M env
0
2
Pebble accretion scenario
2
p 0.07 g/cm , r=10 AU
4
6
t /Myr
8
10
9
9
The critical core mass
Lambrechts et al 2014
- Protoplanetary disc lifetimes constrain
accretion rates to be high to complete
cores
- critical core mass increase with
accretion rate (Rafikov 2006)
- The high accretion rates necessary to
form the cores lead to core masses
much too large compared to the gas
giants in the Solar System
- Therefore halting the accretion is a
necessity in the core accretion
scenario (or a lot of ice pollution)
10
10
The pebble isolation mass
50
Core
growth
40
Runaway
gas accretion
Envelope
contraction
M /ME
30
20
M iso
Mc
M env
10
p
0.07 g/cm2 , r=10 AU
Pebble accretion scenario
0
0
2
4
t /Myr
Miso
✓ ◆3
⇣ r ⌘3/4
H
⇡ 20
ME / r
5AU
- gravity of the core perturbs gas disc
- creates a pressure bump (shallow gap)
that traps particles outside the accretion radius,
thereby halting solid accretion
- pebble isolation mass ~ critical core mass
11
11
Ice giant / gas giant divide
Jupiter
Saturn
Uranus
Neptune
- radial and compositional dichotomy
between gas and ice giants
- gas giants in the inner disc (<10 AU)
reach isolation and therefore undergo
runaway gas accretion
- ice giants have not undergone isolation
(or only briefly). The blue lines show the
least polluted envelope that can be bound
to the core.
12
Lambrechts et al 2014
12
Exoplanets with envelopes
R /RE
101
H2
100
H2 O
SiO2
10-1
100
101
102
103
104
M /ME
Data from open exoplanets catalogue
13
13
Expanding the scenario
1.
2.
3.
10-4 ME
0.01-10ME
• full disc models see following talk by Bertram Bitsch
• terrestrial embryo/planet formation
(Guillot+2014, Johansen+2015, Morbidelli+2015, Levison/Kretke group+2015, Lambrechts in prep)
• (hybrid) N-body codes
Kretke & Levison, 2014, Levison+2015 , Chambers, 2014, and above
50
• doing the gas envelope contraction
14
Mordasini+a,b 2014, Ormel, 2014
Runaway
gas accretion
Envelope
contraction
30
M /ME
carefully Piso & Youdin 2014,
Core
growth
40
20
M iso
Mc
M env
10
p
0.07 g/cm2 , r=10 AU
Pebble accretion scenario
0
0
2
4
t /Myr
14
Questions?
• formation in a few Myr
• halting solid accretion (~20 Me)
form gas giants and ice giants
• dust-to-planet efficiency (~50%)
• metallicity correlation (steep)
• overcome type I migration
15
Lambrechts & Johansen, 2014
Lambrechts, Johansen, Morbidelli, 2014
Lambrechts & Johansen, 2012
Morbidelli, Lambrechts +, 2015 submitted
Bitsch, Lambrechts & Johansen, 2015 submitted
15